Synthese (Suppl 5):1-25 (2017)

Authors
Gil Sagi
University of Haifa
Abstract
Tarski characterized logical notions as invariant under permutations of the domain. The outcome, according to Tarski, is that our logic, which is commonly said to be a logic of extension rather than intension, is not even a logic of extension—it is a logic of cardinality. In this paper, I make this idea precise. We look at a scale inspired by Ruth Barcan Marcus of various levels of meaning: extensions, intensions and hyperintensions. On this scale, the lower the level of meaning, the more coarse-grained and less “intensional” it is. I propose to extend this scale to accommodate a level of meaning appropriate for logic. Thus, below the level of extension, we will have a more coarse-grained level of form. I employ a semantic conception of form, adopted from Sher, where forms are features of things “in the world”. Each expression in the language embodies a form, and by the definition we give, forms will be invariant under permutations and thus Tarskian logical notions. I then define the logical terms of a language as those terms whose extension can be determined by their form. Logicality will be shown to be a lower level analogue of rigidity. Using Barcan Marcus’s principles of explicit and implicit extensionality, we are able to characterize purely logical languages as “sub-extensional”, namely, as concerned only with form, and we thus obtain a wider perspective on both logicality and extensionality.
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DOI 10.1007/s11229-017-1447-3
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References found in this work BETA

Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
What Are Logical Notions?Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
The Foundations of Frege’s Logic.Pavel Tichý - 1988 - Berlin and New York: De Gruyter.
Principia Mathematica.A. N. Whitehead & B. Russell - 1927 - Erkenntnis 2 (1):73-75.

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Citations of this work BETA

The Simple Argument for Subclassical Logic.Jc Beall - 2018 - Philosophical Issues 28 (1):30-54.
Hyperintensionality and Normativity.Federico L. G. Faroldi - 2019 - Cham, Switzerland: Springer Verlag.
Invariance Criteria as Meta-Constraints.Gil Sagi - 2022 - Bulletin of Symbolic Logic 28 (1):104-132.
Alfred Tarski.Mario Gómez-Torrente - 2008 - Stanford Encyclopedia of Philosophy.

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